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325_PracticePS4

# 325_PracticePS4 - Department of Economics University of...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Practice Problem Set 4 Professor Sanjay Chugh Spring 2011 1. Optimal Choice in the Consumption-Savings Model with Credit Constraints: A Numerical Analysis. Consider our usual two-period consumption-savings model. Let preferences of the representative consumer be described by the utility function 12 1 2 (, ) , uc c c c E ± where 1 c denotes consumption in period one and 2 c denotes consumption in period two. The parameter is known as the subjective discount factor and measures the consumer's degree of impatience in the sense that the smaller is , the higher the weight the consumer assigns to present consumption relative to future consumption. Assume that 1/1.1. For this particular utility specification, the marginal utility functions are given by 112 1 1 2 ucc c and 212 2 2 c . The representative household has initial real financial wealth (including interest) of 0 (1 ) 1 ra ± . The household earns 1 5 y units of goods in period one and 2 10 y units in period two. The real interest rate paid on assets held from period one to period two equals 10% (i.e., 0.1 r ). a. Calculate the equilibrium levels of consumption in periods one and two ( Hint: Set up the Lagrangian and solve.) b. Suppose now that lenders to this consumer impose credit constraints on the consumer. Specifically, they impose the tightest possible credit constraint – the consumer is not allowed to be in debt at the end of period one, which implies that

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325_PracticePS4 - Department of Economics University of...

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